There are $$$n$$$ islands, numbered $$$1, 2, \ldots, n$$$. Initially, every pair of islands is connected by a bridge. Hence, there are a total of $$$\frac{n (n - 1)}{2}$$$ bridges.

Everule lives on island $$$1$$$ and enjoys visiting the other islands using bridges. Dominater has the power to destroy at most $$$k$$$ bridges to minimize the number of islands that Everule can reach using (possibly multiple) bridges.

Find the minimum number of islands (including island $$$1$$$) that Everule can visit if Dominater destroys bridges optimally.

Input

Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^3$$$) — the number of test cases. The description of the test cases follows.

The first and only line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 100$$$, $$$0 \le k \le \frac{n \cdot (n - 1)}{2}$$$).

Output

For each test case, output the minimum number of islands that Everule can visit if Dominater destroys bridges optimally.

Note

In the first test case, since no bridges can be destroyed, all the islands will be reachable.

In the second test case, you can destroy the bridge between islands $$$1$$$ and $$$2$$$. Everule will not be able to visit island $$$2$$$ but can still visit island $$$1$$$. Therefore, the total number of islands that Everule can visit is $$$1$$$.

In the third test case, Everule always has a way of reaching all islands despite what Dominater does. For example, if Dominater destroyed the bridge between islands $$$1$$$ and $$$2$$$, Everule can still visit island $$$2$$$ by traveling by $$$1 \to 3 \to 2$$$ as the bridges between $$$1$$$ and $$$3$$$, and between $$$3$$$ and $$$2$$$ are not destroyed.

In the fourth test case, you can destroy all bridges since $$$k = \frac{n \cdot (n - 1)}{2}$$$. Everule will be only able to visit $$$1$$$ island (island $$$1$$$).

Destroying Bridges

Examples